The following is taken from the book
Richard Overy, "The Dictators: Hitler's Germany, Stalin's Russia." Penguin Books, 2006.
From pages 194-196:
Those arrested, convicted and sentenced by the NKVD agencies between 1930 and 1953 total 3,851,450. The total executed, according to these figures, was 776,074, which is very close to the figure of 786,098 for those sentenced for execution between 1930 and 1953 published under Gorbachev in 1990. The full record is set out in Table 5.1. These figures are substantially lower than the more speculative pre-glasnost estimates. The statistics for those sent to camps are consistent with what is now known from the archives of the GUlag, about the size and composition of the camp population. In 1940 there were 4 million in the various penal institutions: approximately 1.3 million in the GUlag camps, 300,000 in prison, 997,000 in special settlements and 1.5 million in deportee camps.
By 1950 there were 6.45 million in the various parts of the camp empire. Total deaths in the GUlag camps from 1934 (when accurate records start) to 1953 numbered 1,053,829, in the most part from disease, overwork, frostbite and malnutrition. Some of the NKVD executions were carried out in the camps, and may be double counted in the global total of NKVD killings. More difficult to assess is just how many of the cases tried under the security agencies were in fact criminal cases (like the case of two unfortunate peasant boys sent to mind the collective farm cows, who were caught eating three cucumbers and were each sentenced to eight years in a camp). Nor is it possible to calculate how many cases in the ordinary justice system were in fact raised under Article 58 and punished by execution or imprisonment. The numbers who died in transit to camps, in overcrowded wagons, short of food and water, in sub-zero temperatures can only be hazarded. The full reckoning of the victims of Soviet repression is certainly larger than the figures show, though by hundreds of thousands rather than millions. Executions and camp deaths between them total 1,829,903; this figure should be treated as a minimum. It need hardly be said that aggregate figures mask millions of stories of human suffering beyond the immediate circle of victims: women and men left without a partner, children without parents, families uprooted and loyal friendships obliterated. For the traumas of repression, statistical exactitude is an irrelevance.
Regarding these numbers as the percentage of the Soviet population, according to the official Soviet statistics, the numbers varied between about 150 million (1926) and 180 million (1951).
Thus, the answer to your question is something like 1 in 40.
Lastly, as for "Timur and His Squad," it is just a propaganda lit. (And not bad, if you ignore the backdrop.) A bit more "realistic," is the "The fate of a drummer-boy," by the same author, Arkady Gaidar, and written at about the same time. There, the main character discovers that people pretending to be his relatives are actually spies and is almost killed when he tries to stop them. The moral that this book is designed to convey is that "even your close relatives might be people's enemies." If you want an even scarier macabre story with the same message, read about this boy. Ironically, Arkady Gaidar's grandson, Yegor Gaidar, was the main architect of the controversial shock therapy and market economy reforms administered in Russia after the dissolution of the Soviet Union. Sometimes, life is stranger than fiction.